Solve for $x$ and $y$ using elimination. $\begin{align*}2x-2y &= 5 \\ x+2y &= 6\end{align*}$
We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $3x = 11$ Divide both sides by $3$ and reduce as necessary. $x = \dfrac{11}{3}$ Substitute $\dfrac{11}{3}$ for $x$ in the top equation. $2( \dfrac{11}{3})-2y = 5$ $\dfrac{22}{3}-2y = 5$ $-2y = -\dfrac{7}{3}$ $y = \dfrac{7}{6}$ The solution is $\enspace x = \dfrac{11}{3}, \enspace y = \dfrac{7}{6}$.